Find the 15th Term 2 , 6 , 18 , 54 , 162 , 486 , 1458 , 4374 , 13122 , 39366 , 118098 , 354294 , 1062882

$2$ , $6$ , $18$ , $54$ , $162$ , $486$ , $1458$ , $4374$ , $13122$ , $39366$ , $118098$ , $354294$ , $1062882$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $3$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 3$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = 2$ and $r = 3$ .

$a_{n} = 2 \cdot 3^{n - 1}$

Step 4

Substitute in the value of $n$ to find the $n$ th term.

$a_{15} = 2 \cdot 3^{(15) - 1}$

Step 5

Subtract $1$ from $15$ .

$a_{15} = 2 \cdot 3^{14}$

Step 6

Raise $3$ to the power of $14$ .

$a_{15} = 2 \cdot 4782969$

Step 7

Multiply $2$ by $4782969$ .

$a_{15} = 9565938$

Find the 15th Term 2 , 6 , 18 , 54 , 162 , 486 , 1458 , 4374 , 13122 , 39366 , 118098 , 354294 , 1062882

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